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Math Help - generating an equation for a problem

  1. #1
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    generating an equation for a problem

    I am trying to help my grade 9 daughter solve this problem

    Man has e mail about concert
    Man sends email to 10 friends on day 1 so 10 people know about event
    Each friend send e mail to 2 friends on day 2 so 20 people knows about event
    Each of these 20 people sends email to 2 people on day 3 so 40 knows about event


    Assume there are 5000 people in the town with e-mail and assuming mail only gets forwarded to people who have not already received it , how many days will it take before all 5000 people know about the concert.

    Please kindly show the steps if possible.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by clemkonan View Post
    I am trying to help my grade 9 daughter solve this problem

    Man has e mail about concert
    Man sends email to 10 friends on day 1 so 10 people know about event
    Each friend send e mail to 2 friends on day 2 so 20 people knows about event
    Each of these 20 people sends email to 2 people on day 3 so 40 knows about event


    Assume there are 5000 people in the town with e-mail and assuming mail only gets forwarded to people who have not already received it , how many days will it take before all 5000 people know about the concert.

    Please kindly show the steps if possible.
    -Initially 1 person knows about it
    -Now 10 people know about it

    Series comes out to be

    1,10,20,40,80,160,....

    Leave the first term (ie; leave 1 ) series now is

    10,20,40,80,..

    We need to find the condition "just" when

    1+10+20+40+80+...nth~term \ge 5000

    10+20+40+80+...nth~term \ge 4999

    Now this is a Geometric Progression

    The sum of n terms of a GP
    a, ar, ar^2, ar^3,....ar^n

    is given by

    \frac{a(r^n -1)}{r-1}

    Using this we get

    Sum = \frac{10(2^n-1)}{2-1} \ge 4999

    10(2^n-1)\ge 4999

    <br />
(2^n-1) \ge \frac{4999}{10}

    2^n \ge \frac{5001}{10}

    For n= 9 LHS = 512

    Hence on the 9th day this would be completely spread
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  3. #3
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    In evaluating 2^n -1 the second last equation in your response , would the net effect not be adding +1 to the right hand side so that 4999 becomes 5000?

    Or stated otherwise can you show how you simplified 2^n-1 so that you had 2^n isolated on the left hand side,

    Otherwise I follow and sincere thanks
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by ADARSH View Post
    <br />
(2^n-1) \ge \frac{4999}{10}

    There was a great typo here though the answer remains same, Sorry for it
    Add 1 on both sides

    <br />
(2^n) \ge \frac{4999}{10}+1

    <br />
 (2^n) \ge \frac{4999+10}{10}

    2^n \ge 500.9..........5001/10 is replaced by 5009/10


    For n= 9 LHS = 512

    Hence on the 9th day this would be completely spread
    Red
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  5. #5
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    Generating an Equation for a Problem

    Thanks ADARSH my goal was to demonstrate to the kids that the computer is a great resource and is good for much more than Vibe or Youtube. Yout\r time is greatly appreciated.
    Clemkonan
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